Access proxy server using local proxy server?

I have access to a proxy server on the Internet. Now I want to build a local proxy webserver so that other users can access the remote webserver by sending requests to my (local) proxy server. Is this possible? I tried googling but i think I am missing the keywords? Also is this proxy chaining?
Thanks

Firstly you need to install & configure squid or any other proxy server to be running and using your first proxy server (mostly its done by transparent proxying).

Secondly, I assume you have some server that is used as network gateway to the internet (server that giving access to internet for your users). On it you need to set firewall rules to redirect all www traffic to your proxy. If you dont need to permanently redirect every computer to proxy server you can just add your proxy to browser settings on every computer that needs it.